We review some results about the general Chebyshev polynomials, that is the monic polynomials of least deviation from zero with respect to the supremum norm on compact subsets of the complex plane. We define the n-th Widom factor as the ratio of the norm of the n-th Chebyshev polynomial to the n-th degree of the logarithmic capacity of the set. Our main aim is to consider the asymptotics of the Widom factors for different compact sets.